# Kinetic and potential energy, work and power calculator

> Kinetic energy (½mv²), potential energy (mgh), spring energy, work (Fd cos θ) and power (W/t), solved for any variable, plus the speed after a drop.

ఇంటరాక్టివ్ వెర్షన్: https://www.calcopenly.com/te/science/work-energy-power-calculator
విషయం: విజ్ఞాన శాస్త్ర కాలిక్యులేటర్లు

Six formulas cover the common mechanical-energy problems: kinetic energy ½mv², gravitational potential energy mgh, spring energy ½kx², work Fd cos θ, average power W ÷ t, and the speed after a frictionless drop, √(v₀² + 2gh). Pick one, choose the variable to solve for, and the others become inputs.

Energy comes out in joules, with the kilowatt-hour equivalent beside it from 1 Wh (3,600 J) up; 1 kWh = 3.6 MJ. The default, a 1,000 kg car at 20 m/s (72 km/h), carries 200,000 J, or 0.0556 kWh; at 40 m/s it would carry four times as much.

Potential energy is measured from whichever level you call h = 0, so only differences in height matter. The drop mode ignores friction and air resistance, which makes its speeds an upper limit for real falls.

## ఇన్‌పుట్‌లు

- **Quantity** (ఎంపికలు: Kinetic energy ½mv², Gravitational potential energy mgh, Spring energy ½kx², Work W = Fd·cos θ, Power P = W/t, Speed at the bottom of a drop)
- **Solve for** (ఎంపికలు: శక్తి, ద్రవ్యరాశి, వేగం)
- **Solve for** (ఎంపికలు: శక్తి, ద్రవ్యరాశి, ఎత్తు)
- **Solve for** (ఎంపికలు: శక్తి, Spring constant, Extension)
- **Solve for** (ఎంపికలు: Work, బలం, Distance)
- **Solve for** (ఎంపికలు: సామర్థ్యం, Work or energy, సమయం)
- **Solve for** (ఎంపికలు: Speed at the bottom, Drop height)
- **Energy or work**
- **ద్రవ్యరాశి**
- **వేగం**
- **ఎత్తు**
- **Spring constant k**
- **Extension or compression x**
- **బలం**
- **Distance moved**
- **Angle between force and motion**
- **సమయం**
- **సామర్థ్యం**
- **Speed at the top**
- **Speed at the bottom**
- **Gravitational acceleration**

## ఫలితాలు

- Energy or work (J) — ప్రధాన ఫలితం
- సామర్థ్యం (W)
- Speed at the bottom (m/s)
- ద్రవ్యరాశి (kg)
- వేగం (m/s)
- ఎత్తు (m)
- Spring constant (N/m)
- Extension (m)
- బలం (N)
- Distance (m)
- సమయం (s)
- Energy or work (kWh)

## సూత్రం

$$
KE = \tfrac12 mv^2,\quad PE = mgh,\quad E_s = \tfrac12 kx^2,\quad W = Fd\cos\theta,\quad P = \frac{W}{t},\quad v_b = \sqrt{v_0^2 + 2gh}
$$

## పరిష్కరించిన ఉదాహరణలు

### 1000 kg car at 20 m/s

- Quantity: Kinetic energy ½mv²
- Solve for: శక్తి
- ద్రవ్యరాశి: 1000 kg
- వేగం: 20 m/s
- **Energy or work: 200,000 J**
- **Energy or work: 0.055556 kWh**
- తనిఖీ చేసిన మూలం: Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWh

### Speed of a 0.145 kg ball carrying 100 J

- Quantity: Kinetic energy ½mv²
- Solve for: వేగం
- Energy or work: 100 J
- ద్రవ్యరాశి: 0.145 kg
- **వేగం: 37.1391 m/s**
- తనిఖీ చేసిన మూలం: Python 3.8 decimal: v = √(2E/m) = √(200/0.145) = 37.1390676…

### 50 kg lifted 10 m

- Quantity: Gravitational potential energy mgh
- Solve for: శక్తి
- ద్రవ్యరాశి: 50 kg
- ఎత్తు: 10 m
- **Energy or work: 4,903.33 J**
- తనిఖీ చేసిన మూలం: Python 3.8 decimal: 50 × 9.80665 × 10

### Spring k = 200 N/m compressed 10 cm

- Quantity: Spring energy ½kx²
- Solve for: శక్తి
- Spring constant k: 200 N/m
- Extension or compression x: 10 cm
- **Energy or work: 1 J**
- తనిఖీ చేసిన మూలం: Python 3.8 decimal: ½ × 200 × 0.1² = 1 J

### 100 N at 60° over 5 m

- Quantity: Work W = Fd·cos θ
- Solve for: Work
- బలం: 100 N
- Distance moved: 5 m
- Angle between force and motion: 60 °
- **Energy or work: 250 J**
- తనిఖీ చేసిన మూలం: Python 3.8 math: 100 × 5 × cos60° = 250 J

### Force perpendicular to motion does no work

- Quantity: Work W = Fd·cos θ
- Solve for: Work
- బలం: 100 N
- Distance moved: 5 m
- Angle between force and motion: 90 °
- **Energy or work: 0 J**
- తనిఖీ చేసిన మూలం: W = Fd cos 90° = 0 (OpenStax UP1 §7.1)

## ప్రశ్నలు

### What is the formula for kinetic energy?

Kinetic energy is KE = ½mv²; with mass in kilograms and speed in metres per second the result is in joules. Because speed is squared, doubling it quadruples the energy: a 1,000 kg car has 200 kJ at 20 m/s and 800 kJ at 40 m/s. Rearranged for speed, v = √(2KE ÷ m), so a 0.145 kg ball carrying 100 J moves at 37.1 m/s.

### What is the difference between work and power?

Work is energy transferred by a force, W = Fd cos θ, measured in joules; power is how fast that transfer happens, P = W ÷ t, measured in watts, where 1 W = 1 J/s. Lifting 50 kg through 10 m takes 4,903 J however it is done; doing it in 5 s needs 981 W, and spreading it over 60 s needs 81.7 W.

### How many joules are in a kilowatt-hour or a kilocalorie?

One kilowatt-hour is 3,600,000 J, because it is 1,000 W sustained for 3,600 s. One kilocalorie, the food Calorie, is 4,184 J, using the thermochemical calorie of exactly 4.184 J listed in NIST SP 811. The 200,000 J carried by a 1,000 kg car at 20 m/s is therefore 0.0556 kWh, or about 47.8 kcal.

### How fast does an object hit the ground when dropped?

Without air resistance the impact speed is v = √(2gh), whatever the mass. A drop from 20 m ends at 19.81 m/s (71.3 km/h); a drop from 5 m ends at 9.90 m/s. Speed grows with the square root of height, so four times the height only doubles the speed. Air drag makes real speeds lower, most of all for light objects and long falls.

### How much energy does a spring store?

A spring stores E = ½kx², where k is the spring constant in N/m and x the extension or compression in metres. A 200 N/m spring compressed by 10 cm stores 1 J; compressed by 20 cm it stores 4 J. The formula holds only within the elastic range, where Hooke's law F = kx applies and the spring returns to its original length.

### “Kinetic and potential energy, work and power calculator” ఎంత కచ్చితమైనది?

కచ్చితత్వం మీ ఇన్‌పుట్‌లు, పద్ధతిలోని ఊహలపై ఆధారపడి ఉంటుంది. దశాంశ గణన 50 సార్థక అంకెలను ఉపయోగిస్తుంది. అంచనాలు, సంఖ్యా పద్ధతులు, మూల డేటా తక్కువ కచ్చితత్వంతో ఉండవచ్చు; ప్రదర్శనలో విలువలను రౌండ్ చేయడం ఈ పరిమితులను తొలగించదు. స్వతంత్ర మూలాల పరిష్కారాలతో తనిఖీ చేసిన ఉదాహరణలు: 8. ఉదాహరణకు, “1000 kg car at 20 m/s”ను Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWhతో తనిఖీ చేశారు.

### ఈ పద్ధతికి మూలం ఏమిటి?

OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy; HyperPhysics — Work, energy and power.

## మూలాలు

- [OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy](https://openstax.org/books/university-physics-volume-1/pages/7-introduction)
- [HyperPhysics — Work, energy and power](http://hyperphysics.phy-astr.gsu.edu/hbase/work.html)